Increasing rpm and sounding like its running away means the throttle position sensor may be giving false readings to the EMM, there is slop in the linkage or out of adjustment or there is fuel getting into the crankcase from a flooding vapor separator tank or a leaking fuel pump diaphragm.
Your motor is at least 14 years old and requires complete service annually or at 100 hours. Do you have 14 services on the motor?
Stalling when shifting can be a number of things also.
Have a trained technician do a complete service on the motor paying close attention to the above possiblilties.
"There is never just one thing wrong with a boat";
-- Travis McGee, main character in a book series by John D. McDonald
The factory recommends that a properly trained technician service your Johnson or Evinrude outboard motor. Should you elect to perform repairs yourself, use caution, common sense, and observe safety procedures in the vicinity of flammable liquids, around moving parts, near high-temperature components, and working with electrical or ignition systems.
The information offered here is only general in nature and should not be construed as complete factory approved procedures, techniques, or specifications. Always use the proper service manual for your motor, up-to-date service literature, the correct tools, and have an understanding of how to proceed with troubleshooting and repair methods. If you are unsure or uncomfortable with a procedure, a situation, or a technique, enlist the services of a factory trained technician.